Comparison of volatility function technique for risk-neutral densities estimation

Non-structural approach to implied moments extraction

“…Throughout the recent literature, there are papers using semiparametric and nonparametric approaches for estimating implied probability distribution (Breeden & Litzenberger, 2014;Datta, Londono, & Ross, 2017;Malz, 2014;Smith, 2012;Tavin, 2011), some of them are comparing parametric and nonparametric approaches (Aparicio & Hodges, 1998;Mizrach, 2010;Xiao & Zhou, 2017), while several are dealing with parametric (Arneri c et al, 2015;Cheng, 2010;Gemmill & Saflekos, 2000;Grith & Kr€ atschmer, 2011;Khrapov, 2014;S€ oderlind, 2000;V€ ah€ amaa, 2005) or nonparametric approaches only (Andersen & Wagener, 2002;Bahaludin & Abdullah, 2017;Figlewski, 2009;Grith, H€ ardle, & Schienle, 2011;Jackwerth & Rubinstein, 1996). There are only few papers that compare various non-structural models for implied probability distribution estimation (Bliss & Panigirtzoglou, 2002;Coutant et al, 2001;Gemmill & Saflekos, 2000;Jackwerth, 1999;Jondeau et al, 2007;Jondeau & Rockinger, 2000;Santos & Guerra, 2015).…”

“…This way the out-ofsample performances of the three non-structural models are compared using MSE and DM test. Comparison of the first moments of the distribution and the spot prices at the expiration date of the option, i.e., the forecasting performances, is performed in only few papers (Arneri c et al, 2015;Bahaludin & Abdullah, 2017;Benavides & Mora, 2008), while forecasting accuracy via updated mean and variance on the next trading day is given only in Gemmil and Saflekos (2000). Therefore, literature lacks papers that compare RNDs for forecasting purposes in general and especially for comparison of different non-structural approaches and for different maturity horizons.…”